10) a. A recipe for pizza dough says to use a 10 in. by 14 in. rectangular pan. Jake only has a circular pan with a 12 in. diameter. If Jake makes the pizza in his circular pan, will the crust be thicker or thinner? Explain.
b. Suppose Jake wants to make a round pizza that is exactly the same thickness as the 10 in. by 14 in. pizza in the recipe. What will the diameter of the pan have to be? Is Jake likey to find such a pan? Why or Why not?
I am so confused, please help me!
a. Calculate the area for both pans. The pan with the smaller area will have the thicker crust using the same amount of dough. Remember that the area of a circle = pi r^2 = 3.1416 * r^2.
b. The area of the square pan = 10 * 14 = 140. Then
you would use the folowing equation:
3.1416 * r^2 = 140
This should help you to come to your conclusions. Thanks for asking.
I am having problems understanding how to
solve problems like the following:
a2 + b2 = c2
Please help me where I can understand solving problems such as the one above.
a. To determine whether the crust will be thicker or thinner when using the circular pan, we need to compare the surface area of the rectangular pan to the circular pan.
The surface area of a rectangle is calculated by multiplying the length and the width. In this case, the surface area of the rectangular pan is 10 in. * 14 in. = 140 sq. in.
The surface area of a circle is calculated by multiplying the square of the radius by the constant pi (π). The radius is half the diameter, so the radius of the circular pan is 12 in. / 2 = 6 in. Therefore, the surface area of the circular pan is 6 in. * 6 in. * π = 36π sq. in.
Comparing the surface areas, we have 140 sq. in. for the rectangular pan and 36π sq. in. for the circular pan. Since 140 > 36π, the rectangular pan has a larger surface area, which means the crust will be thicker when using the circular pan.
b. To achieve the same thickness as the 10 in. by 14 in. pizza in the recipe, we need to find the diameter of a circular pan that has a surface area equivalent to 140 sq. in.
The surface area of a circle is given by the formula: A = πr^2, where A represents the surface area and r represents the radius.
We want to find the diameter, which is twice the radius. So, we can rewrite the formula as: A = π(d/2)^2, where d represents the diameter.
We can rearrange the equation to solve for the diameter: d = √(4A/π).
Plugging in the value of A as 140 sq. in., we get: d = √(4*140/π) ≈ √560/π ≈ 10.64 in.
Therefore, to make a round pizza with the same thickness, Jake will need a pan with a diameter of approximately 10.64 inches.
As for whether Jake is likely to find such a pan, it may not be a standard size readily available in most stores. However, there are specialty cooking stores or online platforms where he might be able to find a pan with a diameter close to 10.64 inches. It may require some searching or possibly purchasing a custom-made pan.
a. In order to determine if the crust will be thicker or thinner when using a circular pan instead of a rectangular pan, we need to compare the areas of the two pans. The area of a rectangle is calculated by multiplying its length by its width, while the area of a circle is calculated by multiplying the square of its radius by pi (π = 3.14).
Let's calculate the areas:
Rectangle area = length x width = 10 in. x 14 in. = 140 in²
Circle area = π x radius² = 3.14 x (12 in./2)² = 3.14 x 36 in² ≈ 113.04 in²
Comparing the two areas, we can see that the rectangle has a larger area (140 in²) compared to the circle (113.04 in²). Therefore, the circular pan with a 12 in. diameter will result in a thinner crust because the dough will spread over a larger area.
b. To find the diameter of the pan that will create a round pizza with the same thickness as the rectangular pizza, we need to calculate the area of the rectangular pizza first.
Rectangle area = length x width = 10 in. x 14 in. = 140 in²
Now, let's calculate the radius of the round pizza using the formula for the area of a circle:
Circle area = π x radius²
Substituting the known values:
140 in² = 3.14 x radius²
Solving for the radius:
radius² = 140 in² / 3.14
radius ≈ sqrt(44.59) ≈ 6.68 in.
Finally, to find the diameter, we multiply the radius by 2:
Diameter = 2 x radius = 2 x 6.68 in. ≈ 13.36 in.
Therefore, to make a round pizza of the same thickness as the rectangular pizza in the recipe, Jake would need a pan with a diameter of approximately 13.36 inches.
Regarding whether Jake is likely to find such a pan, it depends on the availability of different sizes of pans in the market. Standard pan sizes are often available in 1-inch increments, so it's possible that Jake may find a pan with a diameter close to 13.36 inches. However, finding an exact match might be challenging since pan sizes can vary and may not align precisely with the required dimensions.